Regarding this dependence of the normalization with the orientation, it is
interesting to note that, in the case of Casimir apparatus in the format of a
box (see, e.g. [1]}), in which case all modes of the field are
discrete, the normalization of the field is insensitive to the orientation,
because these modes do not contribute to the KG product, regardless of the
non-diagonal term in the metric.
